Advance in experimental quantum physics in a laser environment
[1]} and otherwise [2]} challenges measuring from
a physical quantum frame of reference. There are also analyses
on plausible applications of the subject matter, as in Refs.[3]}, [4]}
for examples. The parallel popularity of theoretical studies on
the subject matter and related issues is, for example, well
illustrated by the long lists of references in Refs.[5]}, [6]}, which
are the key background references for our analysis here. We will
refrain from copying over those long lists. Ref.[5]}, following
Ref.[8]}, focuses much on the conceptually simplest and most
fundamentally interesting case of reference frames connected by
a spatial translation in which at least one of the frames is not
classical. Moreover, it gives a completely relational analysis with
interesting and important results. Ref.[6]}, we think, pushes
the particular analysis forwards in an important way. A key
inspiration we have taken over from the reference is to have
a formulation with the reference frame itself taken into account
in the Hilbert space of the relevant states. That allows the
presentation, in the example, of the quantum spatial translation
as the action of a unitary operator within a single Hilbert space,
hence exactly as a symmetry transformation,
all in the language of states as in kets and bras. In the classical
perspective, reference frame transformations are, mathematically,
symmetry transformations as changes of coordinates of the
physical space or phase spaces of physical systems. The totality
of all admissible reference frame transformations that keeps
a dynamical theory invariant is the relativity symmetry. The
latter is considered the most fundamental symmetry, especially
interpreted as one for the physical space or spacetime. The
notion of quantum reference frame transformations asks for
a modification or generalization of the perspective. We are not
talking about a speculative new kind of quantum symmetry,
but what is there in the theory and practical applications of
quantum mechanics awaiting a full understanding. We still see
many important issues left to be addressed properly, both
technically and conceptually. Venturing into the direction is
our target task here. Other interesting papers with closely
related studies include Refs.[10]}, [11]}, [12]}, [13]}.
